Pith Number

pith:V66ZGW27

pith:2017:V66ZGW27BPJ7Y6FCP5IOJVU4VS

not attested not anchored not stored refs pending

Subcritical multitype branching process in random environment

Vitali Wachtel, Vladimir Vatutin

arxiv:1711.07453 v1 · 2017-11-20 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V66ZGW27BPJ7Y6FCP5IOJVU4VS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:30:10.132351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afbd935b5f0bd3fc78a27f50e4d69cac872fca0cd364915084a39ae884d29ff3

Aliases

arxiv: 1711.07453 · arxiv_version: 1711.07453v1 · doi: 10.48550/arxiv.1711.07453 · pith_short_12: V66ZGW27BPJ7 · pith_short_16: V66ZGW27BPJ7Y6FC · pith_short_8: V66ZGW27

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V66ZGW27BPJ7Y6FCP5IOJVU4VS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: afbd935b5f0bd3fc78a27f50e4d69cac872fca0cd364915084a39ae884d29ff3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa6bc8111a9a79a9dcb0bb108301f12736593cadf2c926f39ca9314a3c1ab67a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-11-20T18:30:29Z",
    "title_canon_sha256": "5b4b6d2ca27c3766d2f9cf39d82056ce8ad3f6e85c0526b91e8c5e8306e37bd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.07453",
    "kind": "arxiv",
    "version": 1
  }
}